Question

Простое решение и решение уравнением Тюльпан дешевле розы на 12 рублей. Сколько стоит тюльпан и сколько стоит роза, если вместе они стоят 40 рублей?

Answer 1

Тюльпан-x руб
Роза-x+12 руб
Всего-40 руб
Составляем и решаем уравнение:
x+x+12=40
2x=28
x=14
Т.к. тюльпан стоит 14 руб, то роза 14+12=26 руб
Ответ:тюльпан-14 руб, роза-26 руб.

Answer 2

Пусть х - роза
у - тюльпан
{х+у=40
{х-у=12
решаем сложением:
1) х+у+х-у=40+12
2х=52
х=26
2) если х=26, то у=40-х=40-26=14
Ответ: 26, 14

Answer 3

Problem Analysis

We are given that a tulip is cheaper than a rose by 12 rubles, and the combined cost of a tulip and a rose is 40 rubles. We need to determine the individual prices of the tulip and the rose.

Solution

Let's assume the cost of the tulip is x rubles and the cost of the rose is y rubles.

According to the given information, we have two equations: 1. The tulip is cheaper than the rose by 12 rubles: x = y - 12 2. The combined cost of the tulip and the rose is 40 rubles: x + y = 40

We can solve this system of equations to find the values of x and y.

Solving the Equations

To solve the system of equations, we can use the substitution method or the elimination method. Let's use the substitution method.

From equation 1, we have x = y - 12. We can substitute this value of x into equation 2.

Substituting x = y - 12 into equation 2, we get: (y - 12) + y = 40

Simplifying the equation: 2y - 12 = 40

Adding 12 to both sides of the equation: 2y = 52

Dividing both sides of the equation by 2: y = 26

Now that we have the value of y, we can substitute it back into equation 1 to find the value of x.

Substituting y = 26 into equation 1, we get: x = 26 - 12 x = 14

Answer

Therefore, the tulip costs 14 rubles and the rose costs 26 rubles.

Verification

Let's verify our solution by checking if the given conditions are satisfied.

1. The tulip is cheaper than the rose by 12 rubles: 14 = 26 - 12 (satisfied) 2. The combined cost of the tulip and the rose is 40 rubles: 14 + 26 = 40 (satisfied)

Our solution satisfies both conditions, so we can conclude that the tulip costs 14 rubles and the rose costs 26 rubles.